Edexcel IGCSE Math B 9 Trigonometry

[Maximum number: 3]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

Calculate the length, in cm to 3 significant figures, of BC.

One correct method:
$\tan40^\circ=\frac{10}{BC}$
Equivalently:
$\tan50^\circ=\frac{BC}{10}$
Hence:
$BC=10\tan50^\circ=11.9175\ldots$
Final answer:
$11.9\text{ cm}$

[Maximum number: 7]

Figure for Question 2 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

(a)

Calculate the angle of depression, in degrees to one decimal place, of G from E.

[ 3 ]

Horizontal diagonal:
$DB=\sqrt{4^{2}+3^{2}}=5$
Vertical difference:
2.4-1.5=0.9 $\tan\theta=\frac{0.9}{5}$
Final answer:
$10.2^\circ$
An answer of $79.8^\circ$ gains 2 marks.

(b)

The point P lies on the line GH such that $GP=\frac23GH$ .
The point Q lies on the line BC such that $BQ=\frac23BC$ .
Calculate, in degrees to one decimal place, $\angle APQ$ .

[ 4 ]

$PQ=1.5+\frac23(2.4-1.5)=2.1$ $AQ=\sqrt{4^{2}+2^{2}}=\sqrt{20}$ $\tan\angle APQ=\frac{\sqrt{20}}{2.1}$
Final answer:
$64.8^\circ$
Only allow $65^\circ$ from correct working.

[Maximum number: 1]

The scale drawing opposite shows the positions, A, B and C, of three lighthouses. The points A, B and C lie at sea level in the same horizontal plane with B due north of A.

The scale of the drawing is 1 cm represents 50 km.

(a)

Find by measurement

[ 2 ]

(i)

the bearing of C from A.

Final answer:
$302^\circ\pm2^\circ$

B1.

(b)

Figure for Question (b) — Edexcel IGCSE Math B

Given that S is east of the line AB,

find, by measurement, the bearing of S from A.

[ 1 ]

Final answer:
$016^\circ\text{ to }018^\circ$

[Maximum number: 4]

Figure for Question 4 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

The point P lies on the line GH such that $GP=\frac23GH$ .
The point Q lies on the line BC such that $BQ=\frac23BC$ .
Calculate, in degrees to one decimal place, $\angle APQ$ .

$PQ=1.5+\frac23(2.4-1.5)=2.1$ $AQ=\sqrt{4^{2}+2^{2}}=\sqrt{20}$ $\tan\angle APQ=\frac{\sqrt{20}}{2.1}$
Final answer:
$64.8^\circ$
Only allow $65^\circ$ from correct working.

[Maximum number: 3]

Figure for Question 5 — Edexcel IGCSE Math B

Figure 3 shows a solid right prism ABCDEFGH.
Diagram NOT accurately drawn.
The base of the prism, ABCD, is a rectangle and is horizontal. Trapezium BCHG is a cross section of the prism.
$AB=4\text{ m},\quad BC=3\text{ m},\quad CH=2.4\text{ m},\quad GB=1.5\text{ m}$ $\angle GBC=\angle BCH=\angle ABG=\angle DCH=90^\circ$

Calculate the angle of depression, in degrees to one decimal place, of G from E.

Horizontal diagonal:
$DB=\sqrt{4^{2}+3^{2}}=5$
Vertical difference:
2.4-1.5=0.9 $\tan\theta=\frac{0.9}{5}$
Final answer:
$10.2^\circ$
An answer of $79.8^\circ$ gains 2 marks.

Edexcel IGCSE Math B 9 Trigonometry Questions

Covered syllabus points

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (i)

Question (b)

Question 4

Question 5